Your map shows our friends, partners and allies.
None of them consider themselves to be subjects of the "American Empire".
For one thing, they don't pay us taxes, and for another, their contributions to their own national defense are strictly voluntary.
So it's not, by any reasonable definition, an "empire" and never was.
And yes, friends, partners and allies can well change over the years.
We win some, we lose some, but it has nothing to do with "empire".
"Empire" is just a fantasy.